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Publishing data for analysis from a table containing personal records, while maintaining individual privacy, is a problem of increasing importance today. The traditional approach of de-identifying records is to remove identifying fields such as social security number, name etc. However, recent research has shown that a large fraction of the US population can be identified using non-key attributes (called quasi-identifiers) such as date of birth, gender, and zip code [15]. Sweeney [16] proposed the k-anonymity model for privacy where non-key attributes that leak information are suppressed or generalized so that, for every record in the modified table, there are at least k−1 other records having exactly the same values for quasi-identifiers. We propose a new method for anonymizing data records, where quasi-identifiers of data records are first clustered and then cluster centers are published. To ensure privacy of the data records, we impose the constraint 1 This work was done when the authors were Computer Science PhD students at Stanford University. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. that each cluster must contain no fewer than a pre-specified number of data records. This technique is more general since we have a much larger choice for cluster centers than k-Anonymity. In many cases, it lets us release a lot more information without compromising privacy. We also provide constant-factor approximation algorithms to come up with such a clustering. This is the first set of algorithms for the anonymization problem where the performance is independent of the anonymity parameter k. We further observe that a few outlier points can significantly increase the cost of anonymization. Hence, we extend our algorithms to allow an fraction of points to remain unclustered, i.e., deleted from the anonymized publication. Thus, by not releasing a small fraction of the database records, we can ensure that the data published for analysis has less distortion and hence is more useful. Our approximation algorithms for new clustering objectives are of independent interest and could be applicable in other clustering scenarios as well.

A counting Bloom filter (CBF) generalizes a Bloom filter data structure so as to allow membership queries on a set that can be changing dynamically via insertions and deletions. As with a Bloom filter, a CBF obtains space savings by allowing false positives. We provide a simple hashing-based alternative based on d-left hashing called a d-left CBF (dlCBF). The dlCBF offers the same functionality as a CBF, but uses less space, generally saving a factor of two or more. We describe the construction of dlCBFs, provide an analysis, and demonstrate their effectiveness experimentally.

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In this paper we study the problem of finding the approximate nearest neighbor of a query point in the high dimensional space, focusing on the Euclidean space. The earlier approaches use locality-preserving hash functions (that tend to map nearby points to the same value) to construct several hash tables to ensure that the query point hashes to the same bucket as its nearest neighbor in at least one table. Our approach is differentwe use one (or a few) hash table and hash several randomly chosen points in the neighborhood of the query point showing that at least one of them will hash to the bucket containing its nearest neighbor. We show that the number of randomly chosen points in the neighborhood of the query point q required depends on the entropy of the hash value h(p) of a random point p at the same distance from q at its nearest neighbor, given q and the locality preserving hash function h chosen randomly from the hash family. Precisely, we show that if the entropy I(h(p)|q, h) = M and g is a bound on the probability that two far-off points will hash to the same bucket , then we can find the approximate nearest neighbor in O(n ρ ) time and near linearÕ(n) space where ρ = M/ log(1/g). Alternatively we can build a data structure of sizeÕ(n 1/(1−ρ) ) to answer queries iñ O(d) time. By applying this analysis to the locality preserving hash functions in [17,21,6] and adjusting the parameters we show that the c nearest neighbor can be computed in timeÕ(n ρ ) and near linear space where ρ ≈ 2.06/c as c becomes large.

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In this paper we show how the complexity of performing nearest neighbor (NNS) search on a metric space is related to the expansion of the metric space. Given a metric space we look at the graph obtained by connecting every pair of points within a certain distance r . We then look at various notions of expansion in this graph relating them to the cell probe complexity of NNS for randomized and deterministic, exact and approximate algorithms. For example if the graph has node expansion Φ then we show that any deterministic t-probe data structure for n points must use space S where (St/n) t > Φ. We show similar results for randomized algorithms as well. These relationships can be used to derive most of the known lower bounds in the well known metric spaces such as l 1 , l 2 , l ∞ by simply computing their expansion. In the process, we strengthen and generalize our previous results [18]. Additionally, we unify the approach in [18] and the communication complexity based approach. Our work reduces the problem of proving cell probe lower bounds of near neighbor search to computing the appropriate expansion parameter.In our results, as in all previous results, the dependence on t is weak; that is, the bound drops exponentially in t. We show a much stronger (tight) time-space tradeoff for the class of dynamic low contention data structures. These are data structures that supports updates in the data set and that do not look up any single cell too often.